Born in Mozelos, Aveiro District, Neves grew up supporting Porto and joined the club's youth system at the age of eight.

[9] He played his first match in the UEFA Champions League five days later in a 1–0 win over Lille, and broke another record, previously held by Cristiano Ronaldo, by being the youngest Portuguese to appear in the tournament.

[6][10] On 10 December 2014, during a Champions League group stage fixture against Shakhtar Donetsk, Neves suffered an injury to his right knee following a collision in midfield with Alex Teixeira.

[6] On 20 October 2015, aged 18 years and 221 days, Neves became the youngest player to start as captain in the Champions League, helping Porto to a 2–0 win against Maccabi Tel Aviv in the group stage and surpassing previous record holder Rafael van der Vaart, who held it since 16 September 2003.

[23] In the first match of the new season, he scored his first Premier League goal and assisted Raúl Jiménez in the latter's competitive debut, as his team twice came from behind to draw 2–2 against Everton.

[24][25] His appearance in the match, alongside compatriots Rui Patrício, João Moutinho, Diogo Jota and Hélder Costa, also saw the club break the league record for the most Portuguese players named in a starting line-up.

[19] On 6 October 2018, Neves made his 50th appearance for Wolves and marked the occasion by contributing in the build-up for Matt Doherty's winning goal in a 1–0 victory over Crystal Palace.

[31] On 13 March, his 25th birthday, he assisted the only goal by Coady in a victory at Everton that constituted Wolves's 1,000th win in top-flight football (over 67 seasons dating back to 1888) and also sealed the club's first league double over that opponent since 1972–73.

[38] Neves scored his first goal of the season, and his twenty-fifth in a Wolves shirt, in a 1–1 Premier League draw with Newcastle United at Molineux on 28 August.

[43] Saudi Arabia's Al Hilal confirmed the transfer which set a new record sale for Wolverhampton Wanderers reported to be £47 million.

[47] When the finals began in the Czech Republic, Neves broke a new record by becoming the youngest player to debut for the Portuguese under-21s in the tournament, aged 18 years and 3 months, playing five minutes to help beat England 1–0 in the group stage opener.

His playing attributes also granted him comparisons to Portuguese international teammate João Moutinho for his fine first touch, similar desire to press his opponents and excellent distribution.